The LGA report 'Without a care?' says central government funding has not kept pace with the needs of an ageing population and older people's increasingly complex needs.
And half of councils with social care responsibilities received a government grant increase below inflation this year.
The LGA argues that by switching savings that could be made in the NHS to social care, councils could keep people healthy and out of hospital.
LGA chairman Sandy Bruce-Lockhart said: 'There must be a serious debate about how the care needs of an ageing population are funded. The government does not need to excessively increase public spending. The money is there, it is just in the wrong place.'
The report also reveals that four out of five adults of all ages expect help from their council if they have basic care needs when they reach older age.
This is despite the fact that all of these services could be withdrawn completely by 2009.
The finding is based on research by Ipsos MORI. It asked 967 adults what kind of financial assistance they would expect to receive from their council for basic care to help them live independently at home.
Just 10% of people said they would expect to pay for all their basic care, including help with shopping, cleaning and getting dressed.
Children & Adult